A066791 a(n) = phi(n^2 + n + 1).

1, 2, 6, 12, 12, 30, 42, 36, 72, 72, 72, 108, 156, 120, 210, 240, 144, 306, 294, 252, 420, 462, 312, 468, 600, 360, 648, 756, 540, 792, 756, 660, 900, 1122, 792, 1152, 1260, 792, 1482, 1332, 1092, 1722, 1656, 1260, 1692, 1944, 1224, 2160, 2160, 1512, 2550, 2268

Offset

0,2

Comments

For n > 1, a(n) is a multiple of 6. More generally, phi(n^(2*k) + n^k + 1) is a multiple of 6*k for all n > 1 and k >= 1. - Max Alekseyev, Sep 24 2024

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000 (terms n = 1..1000 from Harry J. Smith)

Formula

a(n) = A000010(A002061(n+1)). - Alois P. Heinz, Sep 24 2024

Sum_{k=1..n} a(k) = c * n^3 + O((n*log(n))^2), where c = (8/27) * Product_{primes p == 1 (mod 3)} (1 - 2/p^2) = 0.27699022627... . - Amiram Eldar, Dec 09 2024

Mathematica

Table[EulerPhi[n^2+n+1], {n, 60}] (* Harvey P. Dale, May 06 2013 *)

Prog

(PARI) a(n) = eulerphi(n^2 + n + 1); \\ Harry J. Smith, Mar 27 2010

Crossrefs

Cf. A000010 (phi), A002061, A376482.

Sequence in context: A058198 A096075 A278256 * A062723 A152667 A145892

Adjacent sequences: A066788 A066789 A066790 * A066792 A066793 A066794

Keyword

nonn,easy

Author

Benoit Cloitre, Jan 18 2002

Extensions

a(0)=1 prepended by Alois P. Heinz, Sep 24 2024

Status

approved